Curry in Haskell

So today I am going to go through the function curry in Haskell. I am finding a hard time trying to understand it and this is my way of trying to understanding it.

First the type signature

This is what I get when I type in :t curry

curry :: ((a, b) -> c) -> a -> b -> c

So what I understand from this is that curry is a function that takes 3 arguments. The first argument is a function and the rest are just values.

The uncurried function

((a,b) -> c)

The function here is what I am mostly interested in because unlike other kinds of functions in Haskell, it takes a tuple of arguments. This tells me one thing - this function cannot be partially applied and both of the arguments must be supplied at the same time.

The other arguments a and b can be ommited because curry itself can be partially applied.

First Conclusion

Furthermore, I can make a conclusion of saying that this how curry's type signature should look:

curry :: ((a, b) -> c) -> (a -> b -> c)

The result of applying a function that takes a tuple as its arguments to curry will result in a function that can be curried.

When I check how curry is defined in Hackage the comment says that :

"curry converts an uncurried function to a curried function."

But curry is defined like so in the Prelude:

curry                   :: ((a, b) -> c) -> a -> b -> c
curry f x y             =  f (x, y)

How does curry expect to turn an uncurried function to a curried function by applying both arguments as a tuple to the uncurried function?

More Investigation

This requires more investigation. I will create my own uncurried function and pass it to curry.

add :: (Int, Int) -> Int
add (x,y) = x + y

So add is a function that takes a takes a tuple of Ints and then adds them together.

I will then apply curry to add.

curry add

The type of the resultant function is:

:t curry add

curry add :: Int -> Int -> Int

The result of applying curry to add results in a function that takes two Int's and returns an Int. Most importantly it is a curried function.

Ray Of Hope

I think this is how the function application would look like based on the definition of curry in the Prelude:

curry add x y = add (x,y)

Even though add itself is never changed, the way it is applied changes because curry gives it the ability to.

let currAdd = curry add

:t currAdd
currAdd :: Int -> Int -> Int

let intermediate = currAdd 1

:t intermediate
intermediate :: Int -> Int

At this point add looks like so:

add(1,y)

All add is waiting for now is another Int so that it can produce the result.

I now get it. curry changes how the function add is applied by giving it the chance of taking one argument at a time instead of both arguments at once. Now that's clever!